Russia's top investigative agency has announced that a government opponent has turned himself in and confessed to orchestrating riots, although the man and his supporters have said he was kidnapped abroad, smuggled back to Russia and then tortured into confessing.

The Investigative Committee of Russia (ICR) said in a statement that Leonid Razvozzhayev admitted to plotting with leftist leaders Sergei Udaltsov and Konstantin Lebedev, and taking funding from a Georgian politician.

A video published on the lifenews.ru website showed Razvozzhayev being taken away from a courthouse on Sunday evening after the court sanctioned his arrest. Razvozzhayev shouted to reporters: "Tell everyone that they tortured me. For two days. They smuggled me in from Ukraine."

The ICR denied his claims, insisting Razvozzhayev himself penned a 10-page confession.

The criminal case against the three activists is based on alleged hidden camera footage aired earlier this month by a Kremlin-friendly TV channel. The documentary claimed they met with Georgian officials to raise money to overthrow Putin's government. The quality of the footage is poor, but investigators insist it was not doctored.

Investigators said on Monday that Razvozzhayev also talked about his involvement in organising clashes between police and protesters in Moscow in May, and said this was funded by Georgian politician Givi Targamadze.

Targamadze has denied any links to funding the Russian opposition.

An opposition rally on 6 May in Moscow turned violent after police restricted access to the square where the rally was to be held. Bottles and pieces of asphalt were hurled at riot police, who struck back by beating protesters with truncheons. The clashes did not appear to have been orchestrated.